Find the cube root of following (a) 64000
(b) 17576
(c) 74088
(d) 59319
(e) 5832
(f) 6859
plz solve this Question in step by step
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Find the cube root of following (a) 64000
(b) 17576
(c) 74088
(d) 59319
(e) 5832
(f) 6859
plz solve this Question in step by step
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Answer:To find the cube root by prime factorization:
In the prime factorization of a perfect cube the factors can be grouped such that is group contains 3 equal prime factors.
Hence, to find the cube root of perfect cube say n , proceed as follows:
1. Find the prime factors of a given number n
2.Form groups of 3 factors such that all three factor in each group are equal.
3.Choose one factor from each group and find the product . This product is the required cube root.
If a group contains one or two equal factor only then a given number cannot be a perfect cube.
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Solution:
[ prime factorization is in the attachments]
i) 64 = 2 x 2 x 2 x 2 x 2 x 2
= 2³ x 2³
³√64 = 2×2=4
ii) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 2³x 2³ x 2³
³√512 = 2×2×2=8
iii) 10648 = 2 x 2 x 2 x 11 x 11 x 11
= 2³ x 11³
³√10648 = 2×11=22
iv) 27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5
= 2³ x 3³ x 5³
³√27000 = 2×3×5=30
v) 15625 = 5 x 5 x 5 x 5 x 5 x 5
= 5³x 5³
³15625 = 5×5=25
vi) 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
= 2³x 2³ x 2³ x 3³
³√13824 = 2×2×2×3=24
vii) 110592 = 2³ x 2³ x 2³ x 2³ x 3³
³√110592 = 2×2×2×2×3=48
viii) 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
= 2³ x 2³ x 3³x 3³
³√46656 = 2×2×3×3=36
ix) 175616 = 2³x 2³ x 2³ x 7³
³√175616 = 2×2×2×7=56
x) 91125 = 5³ x 3³ x 3³
³√91125 = 5×3×3=45
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Step-by-step explanation:
Answer:
ok I will help answer a, 409600000
explain , multiply three time